A generic camshaft adjuster is known, for example from EP 1 979 582 B1. In its basic configuration, the camshaft adjuster includes a stator which is drivable by a crankshaft and a rotor which is rotatably fixedly connected to the camshaft. An annular space is provided between the stator and the rotor, which is divided into a plurality of working chambers by projections which are rotatably fixedly connected to the stator and project radially to the inside, the working chambers each being divided into two pressure chambers by a vane which projects radially outward from the rotor. Depending on the application of a pressure medium to the pressure chambers, the rotor is adjusted with respect to the stator, and the camshaft is adjusted with respect to the crankshaft, in the “advance” or “retard” direction. The pressure buildup of the pressure medium also takes place via the crankshaft, as a result of which only a low pressure medium flow is provided at low rotational speeds. This low pressure medium flow has the disadvantage that, under unfavorable conditions, an undesirable adjustment of the camshaft adjuster may occur, which may subsequently result in an unfavorable operating behavior of the internal combustion engine, in particular in the cold start phase, including unfavorable consumption values with irregular engine running. For this reason, a spiral torsion spring is provided between the rotor and the stator in the camshaft adjuster known from EP 1 979 582 B1. The torsion spring is suspended by a radially outer end on a projection assigned to the stator and by a radially inner end on a pin assigned to the rotor. The spiral spring is secured to the outside by a cover pressed into an annular cylindrical extension of the stator.